Many living things are not in equilibrium for C-14 exchange; the shells of living mollusks show radiocarbon ages of up to 2300 years. The rate of carbon 14 radioactive decay may have been different in the past. The amount of carbon dioxide in the atmosphere may have been different in the past. The assumption of a constant ratio of C-14 to C-12 is invalid; equilibrium would require about 30,000 years, and the C-14/C-12 ratio appears to be increasing still.
The following was extracted from an August 27, 1996 post by Howard Hershey (firstname.lastname@example.org). Additional information was added.
Carbon exists in the atmosphere in the form of carbon dioxide, a gas. It can either be present as stable carbon 12 or unstable carbon 14. Carbon 14 is formed from carbon 12 in the atmosphere by the action of cosmic rays. A steady state results in which the rate of decomposition of carbon 14 is matched by the rate of formation of new C-14 by cosmic rays. The result is that carbon 14 is present as a constant percentage of the total carbon in the atmosphere, although it does change slightly depending upon the amount of cosmic radiation reaching the atmosphere. However, a correction can be made on the basis of carbon 14 readings on items whose age is known from archeological records.
Trees and plants that get their carbon from the carbon dioxide of the atmosphere will, while they are living have a percentage of carbon 14 equal to that in the atmosphere. The same is true of animals that eat plant material. When these organisms die, they no longer ingest C-14 (directly or indirectly) from an atmospheric source. Carbon 14 decays at a particular rate and is not replaced. Thus, measuring the degree to which the carbon 14 level is less than that in the atmosphere provides a measure of time since death.
Mollusks, unlike plants et al., get the carbon for their shells from ancient carbonate and not the atmosphere. Ancient carbon is already depleted in C-14. Therefore mollusk shells are inappropriate for carbon dating because they do not, even when alive, have C-14 at the level present in the atmosphere. The level of C-14 in mollusk shells reflects their source of carbonate.
Creationists assume, usually on the basis of a "flood" argument, that there have been large changes in the amount of carbon dioxide in the atmosphere during the past several thousand years. There probably have been small fluctuations, leading to an uncertainty of plus or minus ten percent, confirmed by dating objects of a known age. However, the evidence does not support the creationist claim of large changes in the amount of carbon dioxide.
The creationist argument that the ratio of C-14 to C-12 is not constant is actually based on the assumption of a young earth with an age of 10,000 years, and sudden changes in the amount of carbon dioxide in the atmosphere caused by the assumed catastrophic events of the Genesis flood. This is the motivation behind the 30,000 year figure quoted in the creationist position.
Creationists attack all radioactive dating with the claim that radioactive decay rates may have been different in the past. There is absolutely no valid evidence to support this claim. It is entirely at odds with everything that is known about nuclear physics.